import java.util.HashMap;

/*
 * @lc app=leetcode.cn id=36 lang=java
 *
 * [36] 有效的数独
 *
 * https://leetcode-cn.com/problems/valid-sudoku/description/
 *
 * algorithms
 * Medium (56.90%)
 * Likes:    252
 * Dislikes: 0
 * Total Accepted:    49.6K
 * Total Submissions: 85.9K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * 判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。
 * 
 * 
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。
 * 
 * 
 * 
 * 
 * 上图是一个部分填充的有效的数独。
 * 
 * 数独部分空格内已填入了数字，空白格用 '.' 表示。
 * 
 * 示例 1:
 * 
 * 输入:
 * [
 * ⁠ ["5","3",".",".","7",".",".",".","."],
 * ⁠ ["6",".",".","1","9","5",".",".","."],
 * ⁠ [".","9","8",".",".",".",".","6","."],
 * ⁠ ["8",".",".",".","6",".",".",".","3"],
 * ⁠ ["4",".",".","8",".","3",".",".","1"],
 * ⁠ ["7",".",".",".","2",".",".",".","6"],
 * ⁠ [".","6",".",".",".",".","2","8","."],
 * ⁠ [".",".",".","4","1","9",".",".","5"],
 * ⁠ [".",".",".",".","8",".",".","7","9"]
 * ]
 * 输出: true
 * 
 * 
 * 示例 2:
 * 
 * 输入:
 * [
 * ["8","3",".",".","7",".",".",".","."],
 * ["6",".",".","1","9","5",".",".","."],
 * [".","9","8",".",".",".",".","6","."],
 * ["8",".",".",".","6",".",".",".","3"],
 * ["4",".",".","8",".","3",".",".","1"],
 * ["7",".",".",".","2",".",".",".","6"],
 * [".","6",".",".",".",".","2","8","."],
 * [".",".",".","4","1","9",".",".","5"],
 * [".",".",".",".","8",".",".","7","9"]
 * ]
 * 输出: false
 * 解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
 * ⁠    但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
 * 
 * 说明:
 * 
 * 
 * 一个有效的数独（部分已被填充）不一定是可解的。
 * 只需要根据以上规则，验证已经填入的数字是否有效即可。
 * 给定数独序列只包含数字 1-9 和字符 '.' 。
 * 给定数独永远是 9x9 形式的。
 * 
 * 
 */

// @lc code=start
class Solution {
    public boolean isValidSudoku(char[][] board) {

        // //解法1：哈希
        // HashMap<Integer, Integer>[] rows = new HashMap[9];
        // HashMap<Integer, Integer>[] cols = new HashMap[9];
        // HashMap<Integer, Integer>[] boxs = new HashMap[9];

        // for (int i = 0; i < 9; i++) {
        //     rows[i] = new HashMap();
        //     cols[i] = new HashMap();
        //     boxs[i] = new HashMap();
        // }

        // for (int i = 0; i < 9; i++) {
        //     for (int j = 0; j < 9; j++) {
        //         if (board[i][j] == '.')
        //             continue;
        //         int box = (i / 3) * 3 + j / 3;
        //         int val = (int) board[i][j];
        //         rows[i].put(val, rows[i].getOrDefault(val, 0) + 1);
        //         cols[j].put(val, cols[j].getOrDefault(val, 0) + 1);
        //         boxs[box].put(val, boxs[box].getOrDefault(val, 0) + 1);

        //         if (rows[i].get(val) > 1 || cols[j].get(val) > 1 || boxs[box].get(val) > 1)
        //             return false;
        //     }
        // }
        // return true;

        // // 解法2： set
        // Set seen = new HashSet();
        // for (int i = 0; i < 9; i++) {
        //     for (int j = 0; j < 9; j++) {
        //         char c = board[i][j];
        //         if (c == '.')
        //             continue;
        //         if (!seen.add(c + " in row " + i) || !seen.add(c + " in column " + j)
        //                 || !seen.add(c + " in block " + i / 3 + "-" + j / 3))
        //             return false;
        //     }
        // }
        // return true;

        // 解法3：dp
        char[][][] arr = new char[9][9][3];
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] == '.')
                    continue;
                int box = (i / 3) * 3 + j / 3;
                int val = (int) (board[i][j] - '1');

                if (arr[i][val][0] == 1 || arr[j][val][1] == 1 || arr[box][val][2] == 1)
                    return false;

                arr[i][val][0] = 1;
                arr[j][val][1] = 1;
                arr[box][val][2] = 1;
            }
        }
        return true;

        return backtrack(board, 0, 0);
    }

    boolean backtrack(char[][] board, int i, int j) {
        int m = 9, n = 9;
        if (j == n) {
            return backtrack(board, i + 1, 0);
        }
        if (i == m) {
            return true;
        }
        if (board[i][j] != '.') {
            return backtrack(board, i, j + 1);
        }
        for (char ch = '1'; ch <= '9'; ch++) {
            if (!isValid(board, i, j, ch)) {
                continue;
            }
            board[i][j] = ch;

            if (backtrack(board, i, j + 1)) {
                return true;
            }

            board[i][j] = '.';
        }
        return false;
    }

    boolean isValid(char[][] board, int r, int c, char ch) {
        for (int i = 0; i < 9; i++) {
            if (board[r][i] == ch)
                return false;
            if (board[i][c] == ch)
                return false;
            if (board[(r / 3) * 3 + i / 3][(c / 3) * 3 + i % 3] == ch)
                return false;
        }
        return true;
    }
}
// @lc code=end
